Wiener Indices in Random Cyclooctane Chains

The expected values and limiting behaviours for the Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-kirchhoff index of a random cyclooctane chain

“…1. In [22], a cyclooctane chain COC n with n octagons O 1 , O 2 , • • •, O n is considered as a situation that a new terminal octagon connects by an edge to a cyclooctane chain COC n−1 as given in Fig. 2.…”

“…Motivated by [22,23,28,29], the rest of the paper is organized as follows. In section 2, we determine the explicit formulas of E Gut(COC n ) and E S(COC n ) for random cyclooctane chains.…”

Comparison of the Wiener and Kirchhoff Indices of Random Pentachains

“…Yang and Zhang [15] studied the Wiener indices of random polyphenyl chain graphs in 2012. Wei et al [44,50,51] obtained simple formulae for the expected value of the Wiener indices of random polygonal chains. Wang et al [43] studied the expected value of the Wiener indices of random alpha-pentachains.…”

The expected values, variances and limiting distributions of Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index for a class of random chain networks

“…At the same way, Zhang, Li, Li and Zhang [44] obtained the simple formulas of E Gut(G n ) , E S(G n ) , E Kf * (G n ) and E Kf + (G n ) for a class of random chain networks. Motivated by [44][45][46][47][48], for this article, in section 2, we determine the explicit formulas of E Gut(P G n ) , E S(P G n ) , E Kf * (P G n ) and E Kf + (P G n ) for the random chain networks. In section 3, we obtain explicit formulas of V ar Gut(P G n ) , V ar S(P G n ) , V ar Kf * (P G n ) and V ar Kf + (P G n ) based on the known results of others' paper, and prove that these four indices of the random chain networks asymptotically obey normal distributions.…”